THREE-DIMENSIONAL PRINTING SYSTEM INCLUDING THREE-DIMENSIONAL PRINTING APPARATUS AND SUPPORT ARRANGEMENT DETERMINING APPARATUS, AND METHOD of DETERMINING SUPPORT ARRANGEMENT

1. A three-dimensional printing system comprising: a three-dimensional printing apparatus that forms a target object and supports; and a support arrangement determining apparatus that determines a position arrangement of the supports, for use with the three-dimensional printing apparatus wherein the supports are attached and arranged on the target object to be formed to form the target object and the supports, the support arrangement determining apparatus including: a storing processor configured or programmed to store data of a three-dimensional model of the target object; a reference processor configured or programmed to shift and rotate the three-dimensional model stored in the storing processor so as to set the three-dimensional model into a predetermined reference position and orientation; a center-of-gravity calculating processor configured or programmed to calculate a center of gravity of the three-dimensional model; a principal axis setting processor configured or programmed to calculate, among points on outer circumferential surfaces of the three-dimensional model, a farthest point that is most distant from the center of gravity of the three-dimensional model calculated by the center-of-gravity calculating processor, and set a principal axis connecting the center of gravity of the three-dimensional model and the farthest point; a tilting processor configured or programmed to tilt the three-dimensional model set in the predetermined reference position and orientation by the reference processor so that the principal axis set by the principal axis setting processor is parallel or substantially parallel to a horizontal plane; and an arranging processor configured or programmed to attach and arrange the supports on a top surface or a bottom surface of the three-dimensional model tilted by the tilting processor, wherein the three-dimensional printing apparatus forms the target object based on the three-dimensional model tilted by the tilting processor, and the three-dimensional printing apparatus forms the supports as attached and arranged by the arranging processor.

2. The three-dimensional printing system according to claim 1 , further comprising: a rotation processor configured or programmed to calculate a nearest point that is a closest point to the center of gravity of the three-dimensional model among the points on the outer circumferential surfaces of the three-dimensional model tilted by the tilting processor, and rotate the three-dimensional model around the principal axis so as to set the nearest point into a position that overlaps the principal axis when viewed in a plan view; wherein the arranging processor is configured or programmed to attach and arrange the supports on one of the top surface and the bottom surface on which the nearest point is positioned in the three-dimensional model tilted by the tilting processor.

3. The three-dimensional printing system according to claim 2 , wherein the target object includes a forbidden surface where the supports are not attached or arranged; and the rotation processor is configured or programmed to calculate the nearest point among the points on the outer circumferential surfaces excluding the forbidden surface.

4. The three-dimensional printing system according to claim 1 , wherein the three-dimensional model is obtained by combining a plurality of polygons; the center-of-gravity calculating processor is configured or programmed to calculate the center of gravity of the three-dimensional model using centers of gravity of the plurality of polygons; and the principal axis setting processor is configured or programmed to calculate respective distances between the center of gravity of the three-dimensional model calculated by the center-of-gravity calculating processor and the centers of gravity of the plurality of polygons, and sets the principal axis into a line connecting the center of gravity of the three-dimensional model and a point at the center of gravity of one of the polygons having a greatest distance between the center of gravity of the three-dimensional model and the centers of gravity of the polygons.

5. The three-dimensional printing system according to claim 1 , further comprising: a pre-processing processor configured or programmed to perform a smoothing process on the three-dimensional model stored in the storing processor; wherein the reference processor is configured or programmed to shift and rotate the three-dimensional model that has been subjected to the smoothing process by the pre-processing processor so as to set the three-dimensional model into a predetermined reference position and orientation.

6. A method of forming a target object and supports including a process of determining an arrangement of the supports, for use with a three-dimensional printing apparatus wherein the supports are attached and arranged on the target object to be formed to form the target object and the supports, for determining a position arrangement of the supports, the method comprising: a storing step of storing data of a three-dimensional model of the target object; a reference step of shifting and rotating the three-dimensional model stored in the storing step so as to be in a predetermined reference position and orientation; a center-of-gravity calculating step of calculating a center of gravity of the three-dimensional model; a principal axis setting step of calculating, among points on outer circumferential surfaces of the three-dimensional model, a farthest point that is most distant from the center of gravity of the three-dimensional model calculated in the center-of-gravity calculating step, and setting a principal axis connecting the center of gravity of the three-dimensional model and the farthest point; a tilting step of tilting the three-dimensional model set in the predetermined reference position and orientation in the reference step so that the principal axis set in the principal axis setting step is parallel or substantially parallel to a horizontal plane; an arranging step of attaching and arranging the supports on a top surface or a bottom surface of the three-dimensional model tilted in the tilting step; and a step of forming, by the three-dimensional printing apparatus, the target object based on the three-dimensional model tilted in the tilting step, and forming the supports attached and arranged in the arranging step.

7. The method according to claim 6 , further comprising: a rotation step of calculating a nearest point that is a closest point from the center of gravity of the three-dimensional model among the points on the outer circumferential surfaces of the three-dimensional model tilted in the tilting step, and rotating the three-dimensional model around the principal axis so as to set the nearest point into a position that overlaps the principal axis when viewed in a plan view; wherein in the arranging step, the supports are attached and arranged on one of the top surface and the bottom surface on which the nearest point is positioned in the three-dimensional model tilted in the tilting step.

8. The method according to claim 7 , wherein the target object includes a forbidden surface where the supports are not attached or arranged; and in the rotation step, the nearest point is calculated among the points on the outer circumferential surfaces excluding the forbidden surface.

9. The method according to claim 6 , wherein the three-dimensional model is obtained by combining a plurality of polygons; in the center-of-gravity calculating step, the center of gravity of the three-dimensional model is calculated using centers of gravity of the plurality of polygons; and in the principal axis setting step, respective distances are calculated between the center of gravity of the three-dimensional model calculated in the center-of-gravity calculating step and the centers of gravity of the plurality of polygons, and the principal axis set to be a line connecting the center of gravity of the three-dimensional model and a point at the center of gravity of one of the polygons having a greatest distance between the center of gravity of the three-dimensional model and the centers of gravity of the polygons.

10. The method according to claim 6 , wherein: a pre-processing step of performing a smoothing process on the three-dimensional model stored in the storing step; wherein in the reference step, the three-dimensional model that has been subjected to the smoothing process in the pre-processing step is shifted and rotated so that the three-dimensional model is in a predetermined reference position and orientation.